= number of miles on the other side.' You bewilder me. The other side of what? `Of the hill,' you say. But then, how did they get home again? However, to accommodate your views we will build a new hostelry at the foot of the hill on the opposite side, and also assume (what I grant you is possible, though it is not necessarily true) that there was no level road at all. Even then you go wrong. You say:
(i) y = 6 ---------
6
----- = 6
4 1/2
I grant you (i), but I deny (ii): it rests on the assumption that to go part of the time at 3 miles an hour, and the rest at 6 miles an hour, comes to the same result as going the whole time at 4 ½ miles an hour. But this would only be true if the `part' were in exact half, i.e. if they went up hill for 3 hours, and down hill for the other 3: which they certainly did not do.
The sixteen who are partially right, are AGNES BAILEY, F. K., FIFEE, G.E.B., H.P., KIT, M.E.T., MYSIE,
A Mother's SON, NAIRAM, A REDRUTHIAN, A SOCIALIST, SPEAR MAIDEN, T. B. C., VIS INERTIAE,
and YAK. Of these, F. K., FIFEE, T.B.C., and VIS INERTIAE do not attempt the second part at all. F. K.
and H. P. give no working. The rest make particular assumptions, such as that there was no level road--
that there were 6 miles of level road--and so on, all leading to particular times being fixed for reaching
the hill-top. The most curious assumption is that of AGNES BAILEY,
x
who says, `Let x = number of
hours occupied in ascent; then---- = hours occupied in descent; and
2
4x
----= hours occupied on the level.' I
suppose you were thinking of the relative rates, up hill and on
3
the level; which we might express by
saying that, if they went xmiles up hill in a certain time, they
4x
would go---- miles on the level in the
same time. You have, in fact, assumed that they took the
3
same time on the level that they took in ascending
the hill. FIFEE assumed that, when the aged knight said they had gone `four miles in the hour' on the
level, he meant that four miles was the distance gone, not merely the rate. This would have been--if
FIFEE will excuse the slang expression--a `sell', ill-suited to the dignity of the hero.
`And now, `descend, ye classic Nine!' who have solved the whole problem, and let me sing your praises. Your names are BLITHE, E. W., L. B., A MARLBOROUGH BOY, O. V. L., PUTNEY WALKER, ROSE, SEA-BREEZE, SIMPLE SUSAN, and MONEY-SPINNER. (These last two I count as one, as they send a joint answer.) ROSE and SIMPLE SUSAN and Co. do not actually state that the hill-top was reached sometime between 6 and 7, but, as they have clearly grasped the fact that a mile, ascended and descended, took the same time as two level miles, I mark them as `right'. A MARLBOROUGH BOY and PUTNEY WALKER deserve honourable mention for their algebraic solutions, being the only two who have perceived that the question leads to an indeterminate equation. E. W. brings a charge of untruthfulness against the aged knight--a serious charge, for he was the very pink of chivalry! She says, `According to the data given, the time at the summit affords no clue to the total distance. It does not enable us to state precisely to an inch how much level and how much hill there was on the road.' `Fair damsel,' the aged knight replies, `--if, as I surmise, thy initials denote Early Womanhood--bethink thee that the word "enable" is thine, not mine. I did but ask the time of reaching the hill-top as my condition for further parley. If now thou wilt not grant that I am a truth-loving man, then will I affirm that those same initials denote Envenomed Wickedness!'
Class List
1. A MARLBOROUGH BOY PUTNEY WALKER
2. BLITHE E.W. L.B. O.V.L. ROSE
SEA-BREEZE SIMPLE SUSAN MONEY-SPINNER
BLITHE has made so ingenious an addition to the problem, and SIMPLE SUSAN and Co. have solved it in such tuneful verse, that I record both their answers in full. I have altered a word or two in Blithe's-- which I trust she will excuse; it did not seem quite clear as it stood.